The function \textcosh(x) , known as the hyperbolic cosine, is defined mathematically as \textcosh(x) = \frace^x + e^{-x}2 . Here, e represents Euler's number, approximately equal to 2.71828. This function is used in various fields, including mathematics and physics, to describe certain types of curves and shapes. The hyperbolic cosine function is similar to the regular cosine function but is based on hyperbolic geometry. It exhibits properties such as being an even function, meaning \textcosh(-x) = \textcosh(x) . This symmetry makes it useful in solving problems involving hyperbolic angles and in modeling real-world phenomena.